Dynamic Analysis of Simply Supported Functionally Graded Nanobeams Subjected to a Moving Force Based on the Nonlocal Euler-Bernoulli Elasticity Theory

Dynamic analysis of simply supported functionally graded nanobeams (FG nanobeams) subjected to a moving force based on the nonlocal Euler-Bernoulli elasticity theory has been investigated in this paper. It is generally believed that the material properties of the functionally graded nanobeams follow the power law change along its thickness. The model of the functionally graded nanobeams with the small deformation is based on the Euler-Bernoulli beam theory, and the governing equations of motion for the dynamic response of the nanobeams, including nonlocal effect, are derived from by the minimum total potential energy principle and the energy variational principle. The higher order partial differential equations have been reduced to a low order partial differential equation by using the Petrov-Galerkin method. The partial differential equations are solved by the employing Runge-Kutta numerical analysis method. Numerical results addressing the significance of the material distribution profile, velocity of the moving force, and nonlocal effect are discussed in detail. The results indicate that these parameters are decisive ones in analysing the dynamic response of the FG nanobeams.